AIMC Topic: Mathematics
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A non-penalty recurrent neural network for solving a class of constrained optimization problems.
Neural networks : the official journal of the International Neural Network Society
Oct 27, 2015
In this paper, we explain a methodology to analyze convergence of some differential inclusion-based neural networks for solving nonsmooth optimization problems. For a general differential inclusion, we show that if its right hand-side set valued map ...
Constructing general partial differential equations using polynomial and neural networks.
Neural networks : the official journal of the International Neural Network Society
Oct 20, 2015
Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transfo...
Generative AI without guardrails can harm learning: Evidence from high school mathematics.
Proceedings of the National Academy of Sciences of the United States of America
Jul 1, 2025
Generative AI is poised to revolutionize how humans work, and has already demonstrated promise in significantly improving human productivity. A key question is how generative AI affects learning-namely, how humans acquire new skills as they perform t...
Navigating Mathematical Basics: A Primer for Deep Learning in Science.
Advances in experimental medicine and biology
Jan 1, 2024
We present a gentle introduction to elementary mathematical notation with the focus of communicating deep learning principles. This is a "math crash course" aimed at quickly enabling scientists with understanding of the building blocks used in many e...
A New Wavelet Collocation Algorithm for Solving a Nonlinear Boundary Value Problem of the Human Corneal Shape.
Nonlinear dynamics, psychology, and life sciences
Oct 1, 2023
The Hermite wavelet method (HWM) is introduced in this study to solve a nonlinear differential equation determining the human corneal morphology. The changes in curvature of the human cornea in hypotony, normal intraocular pressure, glaucoma, and oth...
Survey of semi-tensor product method in robustness analysis on finite systems.
Mathematical biosciences and engineering : MBE
Apr 28, 2023
Recently, the theory of semi-tensor product (STP) method of matrices has received much attention from variety communities covering engineering, economics and industries, etc. This paper describes a detailed survey on some recent applications of the S...
Physics-informed neural networks based on adaptive weighted loss functions for Hamilton-Jacobi equations.
Mathematical biosciences and engineering : MBE
Sep 5, 2022
Physics-informed neural networks (PINN) have lately become a research hotspot in the interdisciplinary field of machine learning and computational mathematics thanks to the flexibility in tackling forward and inverse problems. In this work, we explor...
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